Finite Element (FE) methods are numerical methods for approximating solutions of mathematical differential equations governing a domain such as structure. For example, the differential equations may describe a physical or chemical phenomenon in the structure. FE modeling, which is modeling of a structure based on FE methods, may be used to analyze a response of the structure to a change in, for example, a physical state in the structure. An example is the FE modeling of a structure to analyze deformations and mechanical stresses of the structure under a mechanical load. FE modeling may have applications in various fields. For example, in the medical field, FE modeling may be of interest, for a physician to analyze an anatomical structure shown in a 3D image of a patient. Such FE modeling may help the physician, for example, in diagnosis or surgical planning
In the FE methods which are used in FE modeling, the solution to complex differential equations may be simplified by using an approximation involving a large number of linear equations. This may be similar to an approximation of a circle by a large number of small straight lines. The structure of the problem which may be a line, surface or volume, may be divided into a collection of sub-domains or Finite Elements (for a surface or volume this collection of sub-domains may be referred to as a “mesh”) and the global solution for the structure may be calculated by calculating the solution for each of these sub-domains.
A practical consideration of FE methods is that while the accuracy of the solution may increase with the number of the Finite Elements, the computation power and therefore time or expense required to solve the global solution may increase correspondingly. A pragmatic approach may be to have a fine granularity of sub-domains in regions that are of most interest, and a coarser granularity in regions that are of lesser interest. Therefore regions that are key to any problem, or where the mathematical solution changes rapidly, may be calculated with a finer granularity and regions in a periphery with a coarser granularity.
With respect to FE modeling of anatomical structures, current techniques to generate FE models of anatomical structures, often involve multiple iterations and alterations in order to generate an optimal mesh in the FE models in view of the complex characteristics of anatomical structures. Here, the complexity may stem, for example, from complex geometrical characteristics or boundary conditions. In addition, the user may often be required to manually assess the requirements for obtaining a desired mesh in the FE models, which may be prone to mistake and/or lack of accuracy.